Comparing shapes of high genus surfaces
Differential Geometry
2022-04-19 v3 Metric Geometry
Abstract
In this paper, we define a new metric structure on the shape space of a high genus surface. We introduce a rigorous definition of a shape of a surface and construct a metric based on two energies measuring the area distortion and the angle distortion of a quasiconformal homeomorphism. We show that the energy minimizer in a fixed homotopy class is achieved by a quasiconformal homeomorphism by the lower semicontinuity property of these two energies.
Cite
@article{arxiv.1910.02215,
title = {Comparing shapes of high genus surfaces},
author = {Yanwen Luo},
journal= {arXiv preprint arXiv:1910.02215},
year = {2022}
}
Comments
19 pages, 2 figures. Errors fixed